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Two-loop corrections to the Higgs trilinear coupling in models with extended scalar sectors

The Higgs trilinear coupling $λ_{hhh}$ is of great importance to understand the structure of the Higgs sector and allows searching for indirect signs of Beyond-the-Standard-Model (BSM) physics, even if new states are somehow hidden. In particular, in models with extended Higgs sectors, it is known that non-decouplings effects in BSM-scalar contributions at one loop can cause $λ_{hhh}$ to deviate significantly from its SM prediction, raising the question of what happens at two loops. We review here our calculation of the leading two-loop corrections to $λ_{hhh}$ in an aligned scenario of a Two-Higgs-Doublet Model. We find their typical size to be 10-20% of the one-loop corrections, meaning that they do not modify significantly the one-loop non-decoupling effects, but are not entirely negligible either.